Monge-Amp\`ere Flow for Generative Modeling

Understand

We present a deep generative model, named Monge-Amp\`ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\`ere equation in optimal transport theory.

• The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution.
• Training of the model amounts to solving an optimal control problem.
• The Monge-Amp\`ere flow has tractable likelihoods and supports efficient sampling and inference.